Now personally, I'm not invested in the law and I reject the logical underpinnings of the whole thing. The US is founded on land that already had people on it, that already had multiple systems of authority, so there can be no claim that it has any legal authority to exist at all.
But it's hard to ignore the inconsistency here. Accepting the logic from the Declaration of Independence and the Constitution, there is no way in which the current state can be legitimate and which Trump has the authority to do anything. The last legal president, again, following the logic that assumes such a thing even possible, was Barak Obama. Since the transfer of power, the country has failed to enforce the law.
If the executive cannot complete their oath, then they are considered vacant under the 25th amendment. If the cabinet fails to invoke article 4, then they too are involved in the insurrection (again, simply following the logic outlined pretty clearly here) as are any who would fail to support the invocation.
Since a full takeover of the federal government by insurrectionists wasn't really planned for, I'm guessing that it would necessarily go to the states, being the only remaining legal authority.
Optimization of the multiple sampling and signal extraction in non-destructive exposures
B. Kubik, R. Barbier, A. Castera, E. Chabanat, S. Ferriol, G. Smadja
https://arxiv.org/abs/2506.04904
Food52 co-founder Amanda Hesser is stepping down after 16 years; she launched a Substack newsletter in March that has 705K subscribers (Mark Stenberg/Adweek)
https://www.adweek.com/media/food52-cofounder-amanda-hesser-steps-down/